Towards the understanding of network information processing in biology Open Access

Abstract

Living organisms perform incredibly well in detecting a signal present in the environment. This information processing is achieved near optimally and quite reliably, even though the sources of signals are highly variable and complex. The work in the last few decades has given us a fair understanding of how individual signal processing units like neurons and cell receptors process signals, but the principles of collective information processing on biological networks are far from clear. Information processing in biological networks, like the brain, metabolic circuits, cellular-signaling circuits, etc., involves complex interactions among a large number of units (neurons, receptors). The combinatorially large number of states such a system can exist in makes it impossible to study these systems from the first principles, starting from the interactions between the basic units. The principles of collective information processing on such complex networks can be identified using coarse graining approaches. This could provide insights into the organization and function of complex biological networks. Here I study models of biological networks using continuum dynamics, renormalization, maximum likelihood estimation and information theory. Such coarse graining approaches identify features that are essential for certain processes performed by underlying biological networks. We find that long-range connections in the brain allow for global scale feature detection in a signal. These also suppress the noise and remove any gaps present in the signal. Hierarchical organization with long-range connections leads to large-scale connectivity at low synapse numbers. Time delays can be utilized to separate a mixture of signals with temporal scales. Our observations indicate that the rules in multivariate signal processing are quite different from traditional single unit signal processing.

Table of Contents

Acknowledgements

Contents

List of Figures

1 Introduction ......................................................................................... 1

2 A continuum model of primary visual cortex for contour detection ................. 5

2.1 Introduction........................................................................................ 5

2.2 Continuum model of contour Detection .................................................... 7

2.3 Methods............................................................................................ 11

2.3.1 Image generation............................................................................. 11

2.3.2 Simulations .................................................................................... 12

2.4 Results.............................................................................................. 14

2.5 Discussion.......................................................................................... 17

3 Coarse-graining hierarchical networks ....................................................... 20

3.1 Introduction........................................................................................ 20

3.2 Small-World hyperbolic networks ........................................................... 23

3.3 Review of cluster renormalization in bond percolation ................................ 24

3.3.1 Cluster generating function for MK1 ...................................................... 24

3.3.2 Fixed point analysis for average cluster size .......................................... 25

3.3.3 Scaling behavior near the transition ..................................................... 27

3.4 Cluster-size scaling for hanoi networks ................................................... 28

3.5 Discussion.......................................................................................... 32

4 Accurate sensing of multiple ligands with a single receptor ........................... 34

4.1 Introduction........................................................................................ 34

4.2 Model of ligand-receptor cross-talk ........................................................... 35

4.3 Maximum Likelihood estimate of concentrations ........................................... 36

4.4 Approximatesolution ............................................................................ 37

4.5 Kinetic Proofreading Mechanism for approximate estimation ....................... 41

4.6 Discussion.......................................................................................... 43

5 Extrinsic and intrinsic correlations in molecular information transmission ........ 46

5.1 Introduction........................................................................................ 46

5.2 Background......................................................................................... 47

5.3 Model of two diffusively coupled receptors.................................................... 48

5.4 Solution.............................................................................................. 49

5.4.1 LinearInteractions............................................................................... 49

5.4.2 Non-LinearInteractions ........................................................................ 52

5.5 Discussion............................................................................................ 57

6 Conclusion .............................................................................................. 59

A Appendix ............................................................................................... 61

A.1 Automated graph counting....................................................................... 61

A.1.1 Counting MK1graphlets: ....................................................................... 61

A.1.2 Cluster generating function for HNNP ..................................................... 63

A.1.2.1 Cluster generating function for HN5 ..................................................... 67

Bibliography ............................................................................................... 68

About this Dissertation

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School	Laney Graduate School
Department	Physics
Degree	PhD
Submission	Dissertation
Language	English
Research Field	Physics, Theory
Keyword	computational vision Cellular Signaling Biological Information Processing
Committee Chair / Thesis Advisor	Nemenman, Ilya, Emory University
Committee Members	Family, Fereydoon, Emory University Urazhdin, Sergei , Emory University Goldbart, Paul, Georgia Tech Boettcher, Stefan, Emory University

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