DescriptionA network facilitates the description of selective interactions among the variables of a system. In this work, networks are used to depict selective interactions between molecules, cells, and agents. This research leverages the structure of a network to model biological systems using Ordinary Differential Equations.
The first bio-network investigated is a metabolic network (the nano scale). Metabolism can be captured as a directed graph of nodes and edges. The nodes represent biomolecules or metabolites, and each edge corresponds to a chemical reaction in which the nodes at the tail of the edge are reactants and nodes at the head of the edge are products. The goal is to develop a methodology to accurately simulate large networks. This methodology has been named Linear-In-Flux Expressions (briefly LIFE).
The second class of bio-network investigated is a cell lineage (the micro scale). This is a network of daughter cells from an embryo. The goal is to develop an analytical procedure which can be used on data regarding potential cis-regulatory modules(briefly CRMs) to determine which are active CRMs, as well as where (which cell in the organism) and when (which cell generation) a CRM was active. From this analysis we predict how perturbations of spatial activity will impact the data, and confirm predictions with simulation.
The third class of bio-network investigated is a collection of interacting agents (the macro scale). In opinion formation models, these agents often represent a multidimensional opinion held by an intelligent organism. The goal is to model the evolution of opinions over time as they are influenced by other opinions. Models of this type study the emergence of global patterns driven by local interactions. This work on opinion formation models has two aims: 1. construct a mathematical framework to define classical opinion formation models on the more complex state space of a general compact Riemannian manifold, and 2. investigate the effects of dynamics which govern how influential each agent is.