Relationship Between Network Structure and Emergent Properties in Biological Network Control and Network Hyperuniformity
Restricted (Penn State Only)
- Author:
- Newby, Eli
- Graduate Program:
- Physics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- May 23, 2024
- Committee Members:
- Lingzhou Xue, Outside Unit & Field Member
Dezhe Jin, Major Field Member
David Radice, Major Field Member
Reka Albert, Chair & Dissertation Advisor
Irina Mocioiu, Professor in Charge/Director of Graduate Studies - Keywords:
- Network Science
Hyperuniformity
Network Structure
Complex Systems
Systems Biology
Control Theory - Abstract:
- The field of network science presents a superb avenue for exploring the emergent properties of heterogeneous systems. A network is defined by denoting the disparate elements of the system as nodes and connecting pairs of interacting elements with edges. Through this network representation, we can study the interactions of a complex system and determine how these interactions lead to unexpected outcomes. In many cases, the arrangement of a network’s nodes and edges contains enough information to discern the collective properties that result from the interactions. In this dissertation, I will relate the structure of networks to their emergent properties through two projects: network control and network hyperuniformity. Through network control, we aim to drive a system to a desired state or away from an undesired state in the most efficient manner. In this dissertation, I focus on biological networks at the molecular to cellular level of organization. The various attractors (i.e., stable states) of such networks correspond to cell types, thus network control has important applications in stem cell therapy and cell re-engineering. In biological networks, structural information about the system is relatively well known, while dynamical information is typically incomplete. As a result, it is beneficial to understand how to utilize only the structure of a biological network to control the network. To structurally identify control sets of a network, we extensively evaluate the ability of various structural metrics to rank subsets of the feedback vertex set in how well they control Boolean biological networks. The feedback vertex set of a network is a set of nodes whose removal results in an acyclic network, and has been shown to be able to drive a nonlinear system to its natural attractors. Because the feedback vertex set is typically too large for its control to be experimentally implemented in biological systems and because it may not be always necessary to control the entire feedback vertex set, we focus on identifying which subsets of the feedback vertex set can control the network. We use Boolean models as a test bed of control because they can successfully describe large molecular networks and can qualitatively recapitulate cell state information. From our analysis, we determined that a class of structural metrics we denote as propagation metrics can accurately rank subsets of the feedback vertex set. The subsets that are highly ranked on all propagation metrics are effective at controlling biological networks. We further verify this finding by testing our method on arrays of Boolean models built on random networks whose structures resemble biological networks. On these randomly built networks, we show that there are subsets of the feedback vertex set that can drive a system regardless of the specifics of the Boolean dynamics. This indicates that there are structurally important nodes in biological systems, which we can use to enhance our control of these systems. Thus, we can use the feedback vertex set and propagation metrics to find small, effective control sets of biological networks when we only know the system’s structure. Hyperuniform systems are characterized by the suppression of long-range density fluctuations, and as a result exhibit interesting structural properties. A subclass of these systems, denoted disordered hyperuniform systems, have been shown to depend on the interactions between particles in a system to create global order out of local disorder. Prior research has shown that these disordered hyperuniform systems exist in physics, material science, and biology, and they possess unique photonic and transport properties. Because disordered hyperuniformity is linked to the complex interactions that occur between the elements of each system, we expect that studying hyperuniformity through the lens of network science will be informative for both fields. We extend the hyperuniformity concept to network science by studying the long-range density of different network classes. We build spatial networks from anti-hyperuniform, non-hyperuniform, and hyperuniform point patterns using Delaunay triangulation, and explore how effective various measures are at separating these networks into the correct classes. We first investigate how well the current methods for identifying hyperuniform point patterns extend to networks. Specifically, we investigate if these networks preserve the number variance scaling and bounded hole properties of their respective classes. Our investigation indicates that while the network formalization of these point patterns does distort the distances between points, hyperuniformity can still be identified by analyzing the heterogeneity in the number of nodes in subgraphs or equal area or the heterogeneity in Voronoi cell areas. We also investigate the effectiveness of network science methods at capturing hyperuniformity. Namely, we study various centrality metrics and generalized spanning trees. We show that degree centrality, closeness centrality, and betweenness centrality are all effective at sorting our networks, and that the tortuosity of the backbone of the generalized invasive spanning tree is functionally different between hyperuniform and non-hyperuniform networks. With the introduction of network hyperuniformity and its identification using approaches from both point pattern hyperuniformity and network science, we hope to better understand how the interactions of a system result in an organization that possesses long-range order. Both of the projects in this dissertation showcase how studying a network can reveal unique, and often unanticipated, information about a system’s emergent properties, and how these properties are fundamentally linked to the network’s structure. This dissertation is organized in the following manner: Chapter 1 introduces and gives background on the concepts of network science, network modeling, and hyperuniformity. Chapter 2 introduces network control and details our exploration of structural metrics that can accurately rank FVS subsets. Chapter 3 presents the application of this structural approach to biologically-inspired random Boolean networks. Chapter 4 details ongoing and future projects related to network control. Chapter 5 details network analogs of the methods that can identify hyperuniformity in point patterns and their success on hyperuniform networks. Chapter 6 studies how fruitful network science methods are at identifying and classifying hyperuniform networks. Finally, chapter 7 presents our conclusions from our investigation of network hyperuniformity and exhibits some preliminary results for future approaches to studying network hyperuniformity.