Interaction graphs derived from activation functions and their application to gene regulation

<p>Interaction graphs are graphic representations of complex networks of mutually interacting components. Their main application is in the field of gene regulatory networks, where they are used to visualize how the expression levels of genes activate or inhibit the expression levels of other genes.</p> <p>First we develop a natural transformation of activation functions and their derived interaction graphs, called conjugation, that is related to a natural transformation of signed digraphs called switching isomorphism. This is a useful tool for the analysis of interaction graphs used throughout the rest of the dissertation.</p> <p>We then discuss the question of what restrictions, if any, apply to interaction graphs derived from activation functions. Within these restrictions, we then construct activation functions with any desired interaction graph. The specific case of threshold activation functions, a commonly used kind of activation function, is also considered.</p> <p>We then conclude with some discussion, and new proofs of the conjectures of René Thomas, using the theory of conjugate activation functions. These conjectures relate feedback in the interaction graph to dynamic properties of multi-stationarity and periodic stability. We prove a more general form of Richard and Comet's version of René Thomas' first conjecture. Included is a new counterexample to a local version of Thomas' second conjecture, on only eight components. This is the smallest counterexample that I am currently aware of.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mathematical Sciences

Year dc:date.available

2017

Author dc:creator

• Joyce, Simon

Contributors dc:contributor

• Thomas Zaslavsky

• Pure sciences
• Biological sciences; Applied sciences
• Activation function
• Feedback
• Gene regulatory network
• Interaction
• Signed directed graph
• Switching isomorphism
• Applied Mathematics
• Biology
• Mathematics

Repository record dc:identifier

https://orb.binghamton.edu/dissertation_and_theses/26

OAI identifier oai:identifier

oai:orb.binghamton.edu:dissertation_and_theses-1024