Multi-Dimensional Analysis of Biochemical Network Dynamics Using pyDYVIPAC

Biochemical networks are dynamic, nonlinear, and high-dimensional systems. Realistic kinetic models of biochemical networks often comprise a multitude of kinetic parameters and state variables. Depending on the specific parameter values, a network can display one of a variety of possible dynamic behaviors such as monostable fixed point, damped oscillation, sustained oscillation, and/or bistability. Understanding how a network behaves under a particular parametric condition, and how its behavior changes as the model parameters are varied within the multidimensional parameter space are imperative for gaining a holistic understanding of the network dynamics. Such knowledge helps elucidate the parameter-to-dynamics mapping, uncover how cells make decisions under various pathophysiological contexts, and inform the design of biological circuits with desired behavior, where the latter is critical to the field of synthetic biology. In this chapter, we will present a practical guide to the multidimensional exploration, analysis, and visualization of network dynamics using pyDYVIPAC, which is a tool ideally suited to these purposes implemented in Python. The utility of pyDYVIPAC will be demonstrated using specific examples of biochemical networks with differing structures and dynamic properties via the interactive Jupyter Notebook environment.