Inference, Dynamics, and Coarse-Graining of Large-Scale Biological Networks Open Access
Natale, Joseph (Spring 2020)
Published
Abstract
Theoretical, experimental, and computational developments throughout the past three decades have rendered biological network modeling a powerful mainstay in the toolsets of physicists studying biology (and vice versa). Principal among experimental advancements are the multitude of so-called ``-omics" techniques for gathering high-resolution, system-wide activity data at microscopic scales; on the computational side, they are the complementary abilities to manage and analyze far larger sets of data than ever before. The marriage of these endeavors, in the form of automated network inference, or ``reverse-engineering", has provided an unprecedentedly thorough characterization of small-scale biological systems, but remains costly and ill-equipped to predict the properties or behaviors of those same systems at larger scales. Here we review over two decades' worth of work on network reconstruction, with an eye toward what new knowledge this exciting subfield has brought to modern biology, and then proceed to ask whether the typical products of the reverse-engineering endeavor might not be supplanted by more coarse-grained representations of biological data. Garnering inspiration from dynamical systems theory and statistical mechanics, we first study a random recurrent network model whose dynamics are amenable to a surprisingly compact description in terms of the system's attractors. Then, following classical renormalization group methods in physics, we develop a general framework by which to pass from microscopic to macroscopic descriptions of a network even when the underlying interactions are not yet known. Our generic approach is able to extract appropriate large-scale degrees of freedom, and reproduce other previously established results, for a well-known system in physics. We describe an algorithm that can be applied directly to system-wide activity data, in the hope of obviating the need for explicit network inference as a preliminary step toward learning new biology.
Table of Contents
1 Old Problem, New Solutions; New Problems, Old Solution . . . 1
2 Reverse-Engineering Biological Networks from Large Data Sets . . . 8
2.1 Lay of the land . . . 9
2.1.1 Scale of the biological network inference problem . . . 13
2.1.2 Different ideologies for inference . . . 15
2.1.3 Goals of this Chapter . . . 17
2.2 Roles for reverse-engineering in systems biology research . . . 18
2.2.1 Predictions regarding individual nodes or interactions . . . 20
2.2.2 Insights from the statistical properties of network ensembles . . . 22
2.2.3 Using statistics to characterize or classify individual networks . . . 24
2.2.4 Predicting how a given network will respond to perturbations . . . 25
2.2.5 Representing the joint probability distribution for observables . . . 27
2.2.6 Reconstructions as a part of the Big Picture . . . 29
2.3 Two different meanings of phenomenological “reconstruction” . . . 30
2.3.1 Who talks to whom? Presence, absence of undirected links . . . 31
2.3.2 Who controls whom? Causal relations, directed links . . . 36
2.4 Discussion . . . 48
3 Precise Spatial Memory in Local Random Networks . . . 54
3.1 Introduction . . . 56
3.2 Model and Methods . . . 58
3.3 Results . . . 62
3.3.1 Network supports multiple stable attractors . . . 62
3.3.2 Spatial memories span the entire plane . . . 65
3.3.3 Mutual information is near-optimal for a broad range of parameter values . . . 68
3.4 Discussion . . . 73
4 Coarse-Graining and Renormalization without Locality . . . 79
4.1 Introduction . . . 82
4.2 Motivation and Methodology . . . 86
4.2.1 Real-Space RG within Statistical Physics . . . 86
4.2.2 Algorithm Motivation . . . 89
4.2.3 Description of the Data to be Coarse-Grained . . . 96
4.2.4 Algorithm Outline . . . 99
4.2.5 Note About Validation Procedures . . . 105
4.3 Results . . . 107
4.4 Improving the Quantitative Agreeement . . . 117
4.4.1 Symmetry Breaks in Current Implementation . . . 117
4.4.2 Simple Modifications May Restore Symmetry . . . 120
4.5 Learning New Physics – or Biology (Future Work) . . . 122
5 Outlook: Where Do We Stand? . . . 124
Appendix A Student Research Exercise . . . 129
Appendix B Ising Model Details for Coarse-Graining Analysis . . . 132
Bibliography . . . 139
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