## The underlying pathway structure of biochemical reaction networks

## Timescale analysis of rule-based biochemical reaction networks

## Characterizing Multistationarity Regimes in Biochemical Reaction Networks

## Optimal design of stimulus experiments for robust discrimination of biochemical reaction networks

## Parameter identifiability of biochemical reaction networks in systems biology

## Reconstruction of Arbitrary Biochemical Reaction Networks: A Compressive Sensing Approach

## A scalable method for finding irreducible state-spaces for stochastic models of biochemical reaction networks

## Parametric Sensitivity Analysis for Biochemical Reaction Networks based on Pathwise Information Theory

## Exact results for noise power spectra in linear biochemical reaction networks

## A scalable computational framework for establishing long-term behavior of stochastic reaction networks

## A passivity-based stability criterion for a class of interconnected systems and applications to biochemical reaction networks

## Limitations of the stochastic quasi-steady-state approximation in open biochemical reaction networks

## Design principles of noise-induced oscillation in biochemical reaction networks: II. coupled positive and negative feedback loops

## Multiscale Analysis of Reaction Networks

## Reduction of dynamical biochemical reaction networks in computational biology

## SABRE: A Tool for Stochastic Analysis of Biochemical Reaction Networks

## Quantifying Stochastic Effects in Biochemical Reaction Networks using Partitioned Leaping

## Identifying Biochemical Reaction Networks From Heterogeneous Datasets

## Global Sensitivity Analysis of Biochemical Reaction Networks via Semidefinite Programming

## Time-Scaled Stochastic Input to Biochemical Reaction Networks

Biochemical reaction networks with a sufficiently large number of molecules may be represented as systems of differential equations. Many networks receive inputs that fluctuate continuously in time. These networks may never settle down to a static equilibrium and are of great interest both mathematically and biologically. Biological systems receive inputs that vary on multiple time scales. Hormonal and neural inputs vary on a scale of seconds or minutes; inputs from meals and circadian rhythms vary on a scale of hours or days; and long term environmental changes (such as diet, disease, and pollution) vary on a scale of years. In this thesis, we consider the limiting behavior of networks in which the input is on a different time scale compared to the reaction kinetics within the network.

We prove analytic results of how the variance of reaction rates within a system compares to the variance of the input when the input is on a different time scale than the reaction kinetics within the network. We consider the behavior of simple chains, single species complex networks, reversible chains, and certain classes of non-linear systems with time-scaled stochastic input, as the input speeds up and slows down. In all cases...