Dissertations, Theses, and Capstone Projects

Date of Degree

2-2025

Document Type

Dissertation

Degree Name

Ph.D.

Program

Physics

Advisor

Hernán A. Makse

Committee Members

Wolfram Liebermeister

David J. Schwab

Matthew Y. Sfeir

Vadim Oganesyan

Subject Categories

Bioinformatics | Biological and Chemical Physics | Biophysics | Computational Biology | Physics | Systems Biology

Keywords

Gene Networks, Enzyme Networks, Symmetries, Complexity Reduction

Abstract

The study of biological systems is, inherently, the study of very complex systems. This is essentially due to the fact that they are made up of numerous, often very complicated, interactions between an extensive number of components. Often necessitating an abundance of quantitative parameters and details for a precise description. The human brain for ex- ample, consisting of ∼ 80 billion neurons with ∼ 800 to 100 trillion connections between them, each of them depending on a large set of parameters. Even simpler examples such as bacterial organisms, such as E. coli and B. subtilis, which we focus on in this work, are in fact composed of highly complex interacting systems such as their metabolism and their gene regulation systems, each interacting with one another and with the environment. In the case of gene networks, every interaction between genes is modulated by a number of different microscopic parameters and produces an overall network that is all but impossible to understand. Here we ask the question how can we possibly ”tame” this complexity in order to be able to draw insights and understand these structures. Previous studies have pointed at statistically overrepresented network motifs as building blocks of these structures, however, due to their local nature, they do little to elucidate the overall structure of the network. In addition, the modularity and feed-forward nature relation between modules in the network has also been pointed out, however, they fail to account for the rich variety of feed-back loops existing at the core of these networks. The aim of this work is to present methods, through the use of symmetries, to address the complexity of these systems. In concrete, through the use of graph fibrations, which allow us to identify sets of nodes with isomorphic input history, called fibers, we develop tools that allow us to do a systematic and transparent breakdown of the network into a more intuitive and useful picture. We applied them to the study of gene transcriptional regulatory networks and enzyme networks from the metabolism. The use of these symmetries allows us to reduce the genetic regulatory network of both model bacteria E. coli and B. subtilis to their computational core, relevant for the ”decision-making” processes. In the case of enzyme networks, through the understanding of the symmetry building blocks in these networks and the myriad of feedback loops within these building blocks, we are able to transparently breakdown these immensely complicated networks into biologically relevant modules. Additionally, given that these methods are agnostic as to the type of network they are being applied to, as long as they correspond to any form of message-passing network, the methods proposed here can be generically applied to any such network.

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