Data-Driven Methods for Biological Network Dynamics and Feature Identification

Biological networks are complex and discovering dynamics and underlying features for these large systems can prove difficult if conditions are not favorable. In this dissertation, we begin by reviewing current approaches in data science for dynamical system identification. We pay special attention to methods for inferring dynamical systems which do not require prior knowledge of the symbolic representation of the dynamics, such as Sparse Identification of Nonlinear Dynamics. With these methods in mind, we propose an alternative approach using the Non-negative Least Squares (NNLS) algorithm to infer the dynamics of a (biological) network from data. We will discuss how this approach can be used to identify dynamics for both mass-action systems as well as dynamical systems containing rational functions. On a similar note, we propose a data-driven method for the identification of system conservation law(s) in the absence of the knowledge of system dynamics. Conservation laws are an inherent feature in many systems modeling real world phenomena, in particular, those modeling biological and chemical systems. If the form of the underlying dynamical system is known, linear algebra and algebraic geometry methods can be used to identify the conservation laws. We develop a robust data-driven computational framework that automates the process of identifying the number and type of the conservation law(s) while keeping the amount of required data to a minimum. We demonstrate that due to relative stability of singular vectors to noise we are able to reconstruct correct conservation laws without the need for excessive parameter tuning. While we focus primarily on biological examples, the framework proposed herein is suitable for a variety of data science applications and can be coupled with other machine learning approaches. Finally, we extend conditions for adaptation for biological networks to include singular systems with non-hyperbolic equilibria and conditions in which this alternative criteria are needed. The proposed theoretical extension is compatible with the notions of homeostasis and robust perfect adaptation (RPA) and clarifies the relationship between the two. The new condition is derived using the notion of Moore-Penrose pseudoinverse and is implemented using a numerically efficient algorithm. The proposed approach is tested on several synthetic systems that are shown to exhibit homeostatic behavior yet lie outside of the scope of earlier work.

Author

• Oellerich, Tracey Gene

• Adaptation
• Biological Networks
• Conservation Laws
• Data-driven
• Ordinary Dynamical Systems
• Singular Value Decomposition

Identifier

hdl:1920/14375

OAI identifier oai:identifier

oai:MARS:1920/14375